Preheat the oven to 425°F (220°C).
In a large bowl, combine the melted butter, minced garlic, Old Bay seasoning, smoked paprika, cayenne pepper, salt, and black pepper. Stir well to create the seasoning butter.
Add the halved baby potatoes to the bowl and toss to coat evenly with the seasoning butter.
Spread the potatoes in a single layer on a large sheet pan. Roast in the preheated oven for 10 minutes.
Remove the sheet pan from the oven. Add the corn pieces and sliced andouille sausage to the pan. Toss everything gently to combine and spread out evenly.
Return the sheet pan to the oven and roast for an additional 7 minutes.
Remove the sheet pan again and add the shrimp. Toss the shrimp with the ingredients on the pan to coat them with the seasoning butter.
Roast for a final 3 to 5 minutes, or until the shrimp are pink and opaque and the potatoes are tender when pierced with a fork.
Remove from the oven and sprinkle the chopped fresh parsley over the top.
Serve immediately with lemon wedges on the side for squeezing over the shrimp boil.